This guide is likely outdated, as it was created around the time of the Carnelian update when Sunless Sea was in early access. Whilst most of the information in this guide will likely still apply, some of it may not.

First of all, you should spend what you can on fuel and supplies. Because you have a small crew, and because supplies are easier to come by, you should buy more fuel than supplies. Contrary to popular belief, buying and selling Casks of Mushroom wine is NOT an efficient way to make money; it is a grind where you loose money to fuel and supplied each journey, so don't do that. Also get a mission from the admirality survey office. Usually the first mission is somewhere distant but simple, and not terrible difficult to get to, such as Iron & Misery Co. Funging Station, or Station III, but this can wait for a bit. Pay attention to the directions they give you (e.g. "Somewhere Southeast of London"), as it will help you find the location of the isalnd. These quests will give you Strategic Information when you visit the location, which can be exchanged for 150 Echoes. Before you depart Choose the option that will allow you to take tomb colonists north to Venderbight, for a little bit of extra cash.
Stop off at Hunter's Keep on the way and take a report, as that will net you a bit extra as well. If you have a random event (Something awaits you in port) available, you can meet up with the sisters who will give you free supplies, reduce your hunter, and may reduce terror; The first sister will give you one terror and a Tale of Terror!, the second sister will greatly reduce terror (about 10-15), and the third will slightly reduce terror (~5) and give you a Memory of Distant Shores. You can also use up a Recent News if you don't have anything awaiting you in port. Revisiting this place can be an efficient way of reducing terror. For a while.
You'll probably encounter a pirate and some bat sworms on your way there, which aren't too tough and give free supplies. When you reach Venderbight, sell the Tomb Colonists at the shop, explore the place a bit (you'll probably get a complicated-looking quest, but don't worry about it.) And then set sail west. Where exactly? Wherever. Exploring is a massive part of this game, and because a lot of the islands are randomly located, it can be difficult to pinpoint them all. Don't go north, though; There's probably nothing interesting up there for you yet. Except living icebergs that willkill you.
Make your way back to Fallen London when your fuel is getting a bit low (maybe about 5) and you'll have some events waiting for you; namely the Blind Bruiser and the Merchant Venturer. The Blind Bruiser will offer you free fuel and supplies as 'dispensation'; Whilst he is a shady fellow, I reccomend you take them; You'll be pretty much set for your next venture into the Zee, but you might have to do a few errands for him. Make sure to hand in your port reports and strategic info if you have it. If you've got the money, buy a better weapon, don't buy a new engine unless you have the money; It will burn through fuel quicker. Now, set off to explore once again.

Whilst supplies are usually easy to come buy and slow(ish) to run out, fuel is a different matter, and links together with Terror. Leaving your prow light on will reduce terror build but also greatly drain your fuel, whereas leaving it off will save your fuel but your sanity will suffer greatly; therefore it is important to balance the two, and maintaining these can also help with your overall survival against the terrors of the Zee.

Generally, you should only use your prow light when absolutely necessary, such as when travelling through an especially dark area with no islands or buoys nearby. If you leave it off during these scenarios you will take massive blows to your sanity, which can be worse than wasting your fuel.

A little trick I have found is that, where possible, you can 'hug' the edges of islands, rocks, and sometimes scenery, to lower the effects of terror buildup. Whilst doing this, I reccomend you turn your prow light off, unless you desperately need your sanity, as it sets the buildup to 2 as opposed to 3, which is the worst. Doing so will save fuel and lower your terror buildup, a win-win.

Early in the game, you will not want to face opponents head-on. Most of the time, you wont want to face them at all. If you come across an especially difficult opponent such as a Lifeberg or a Faustic Corsair, your best course of action is to turn off your prow light, regardless of where you are, and try to maneuver around them. The drain to sanity you will take is a lot less fatal than damage to your hull. Because that can kill you. And that's not good. Just stay out of their line of sight or where they are travelling, and you should be OK. And if you are spotted, turn on full power and sail away as fast as you can, and hope your engine doesn't blow up.

The shadows can also be a great use to you in combat; If you sneak up behind an enemy with your prow light off, you can get several shots off before they have maneuvered to face you. An efficient method of combat is this:

• Keep your prow light off at all times if they haven't spotted you
  
• Try to keep the enemy distant; at the edge of your weapon arc
  
• Constantly back up, because they will constantly advance
  
• Use the environment to your advantage, for cover and sanity.
  
• If fighting a ship, try to maneuver around them and flank them from behind if you can.
  
• If they spot you, turn on your prow light and get them in the beam as it will let you aim faster.
  
• Stay away from Mount Nomad.

will upload screenshots later

With the recent Carnelian update, making money has become much simpler with the Merchant Venturer; he will give you a choice of two products he is looking for, and buy them from you at a higher price than you can get from selling them at the Bazaar, and will often give you double what you payed for them, if you did indeed pay for them. Below is a list of the goods he will request, and the ease of getting them. (Unfortunately I don't know the details of some of them or the amount of money he will give you, and some may be impossible to get, and may therefore be a dead-end if you're unlucky.)

7 Scintillack
To my knowledge, Scintillack can only be found in Port Cecil, usually far to the east of London, and even then it cannot be directly bought; It can only be acquired through a random event or through a quest that requires you to win all games of Chess which requires high veils or mirrors (I forget which one), and progress on a quest takes you to the Salt Lions and back. During the quest, you can exchange certain items such as hunting trophies and stygian ivory for a big bunch of scintillack, which may take up a lot of room in your ship if you go there early on. It is best avoided if possible. If I remember correctly the merchant will give you 1000 echoes for these, if you manage to get them.

7 Devilbone Dice
These can be bought from Mount Palmerston, usually to the north-east of London. These are one of the easier products to obtain, provided you avoid the Faustic Corsairs. This is one of the most profitable offers he will give you, as Devilbone dice only cost 20 echoes each and he pays 500 for the lot, netting you a profit of 360 echoes. A good choice.

7 Zzoup
Along with Devilbone dice, Zzoup can also be bought at Mt. Palmerston for 70 echoes each. Unfortunately, I can't remember the exact amount of money he will give you, but it's probably either 700 or 1000. If it's 700 you would make a profit of 210 echoes, and if it's 1000 you would make a profit of 510 echoes.

7 Sacks of Darkdrop Coffee Beans
Whilst the merchant will reccomend you go south to some places I can't remember the name of to buy these, they have not been implimented yet, so they sell them at the same price as the Bazaar at London, which you can buy them from. You can easily buy the beans from london and give them to him on the spot for a quick bit of cash.

7 Mutersalt
Possible the worst choice he can give you. Currently, the only way to get Mutersalt is by travelling to Wither, far to the north of London. But the biggest problem is that they cannot be bought with money. The only way to purchase them is by trading Zee-stories, which are very difficult to come across early on in the game. Travelling to wither for this choice isn't worth it anyway; there are more efficient ways to spend your Zee-stories in Wither.

7 Romantic Literature
This is a tricky choice; there are only two ways to find these, and neither of them are easy. The first way is to sail to Khan's Heart far to the east where is is sold in the Nephrite Quarter, but you can't buy them from there unless you have a Nephrite ring. And to my knowledge, the only way to get one is by gifting LOTSof Darkdrop Coffee Beans to Khan's Glory. Which can be VERY expensive, and more trouble than it's worth. The other way is by going very far southeast to the Uttershroom with Firkins of Prisoner's Honey and exchanging them for Docile Blemingtons. Whilst they have other properties, they can apparantly be traded at London; Two blemingtons for one romantic literature. Probably more trouble than it's worth.

7 Hunting Trophy
Simple in theory, possibly difficult in practice. To get these, you have to find and kill some mildly strong monsters such as Bound Sharks and Albino Morrays. Luckily you won't have to pay any Echoes from them, but your time fighting them at Zee may take a toll on your sanity. Be cautious.

21 Bolts of Spider Silk
Yes. Twenty-one. Available only from Khan's Heart (with the Nephrite Ring) or at the Bazaar for 100 echoes each. I can't remember what he gives you for them, but I doubt it's worth it.

7 Bales of Parabola-Linen
Whilst they can be bought from the Bazaar at 120 echoes each, they are apparantly sold much more cheaply at the Iron Republic, which is always south along the coast from London. You may need to do a few events there for the shop to change, but if it is cheaper there, great. Will need verification.

5(?) Lamentable Relics
This can be tricky to do, as there is nowhere that garantee's a Lamentable Relic drop. They can be occasionally found in Venderbight when Something Awaits you in Port, but otherwise I'm not sure where else to find them. Could be tricky.
After more exploring I've discovered that you can get a bunch at Godfall if you have decent stats and a good amount of Foxfire Candles. But that could also be tricky.

1 Colossal Fluke-Core
This object can only be acquired by killing a Lorn-Fluke, often found deep in the southeast. Whilst only one is needed, they can be a challenge early on, as they have both a ranged attack and a melee attack. Could be worth a try.

There is one other option, which to my knowledge has not been implimented yet.

Also please be aware that you can only do trade missions for the Merchant Venture ten times; after which, he will request you take him to the Avid Horizon, a desolate place far to the Northeast, which you can only do if you have fourty spaces of inventory free, an impossibility with the starting ship. With any luck, you'll have made enough money to afford a better one. If you can't do this, he'll simply give you some secrets and be on his way. However, if you are fortunate enough to have the space and the time, you may get a Searing Enigma for free.
And if you have 50 hearts and a Searing Enigma of your own, something special may await you...
...or something dreadful.

Rather than do chores based on luck and chance, you can opt to use methods that are garanteed to net you a fixed amount of profit, some more profitabe and efficient than others.

• Deliver Clay men from Polythreme to Fallen London
  Polythreme is a fairly perilous place, with Unfinished Pirates often roaming the shores near the island. The island itself is often a fair distance to the east-south-east, and at 120 echoes for all 6 given to you, it's probably not worth it either.
  
• Deliver Sphinxstone from the Salt Lions to Fallen London
  Whilst this is less of a chore, as the Salt Lions are rarely far from London, it can be a burden on your cargo, as you need 20 free spaces to deliver them. You also need 200 echoes to purchase the initial load, but you get 500 echoes when you sell them at London, giving you a profit of 300 echoes. The salt lions also ties in with the third method...
  
• Explore the Wisp-Ways of the Mangrove College
  This option is based both on luck and skill. The Mangrove College tends to be somewhere in the east or southeast, and requires a few supplies and a fair amount of Foxfire Candles to explore, but you can usually get several supplies for free their if Something Awaits you in Port. With good stats and good luck you can find Searing Enigmas, Captivating Treasures, Blue Scintillack and other goodies. However, there is no guarantee, and you may loose sailors or become wounded along the way.
  
• Deliver a Searing Enigma to the Alarming Scholar
  This is arguably one of the most efficient and reliable methods of accumulating money in the game. The Alarming Scholar will give you a good amount of money for several oddities and artifacts, and the Searing Enigma is one of them.
  
  1. With one Zee-story, go north along the coast to Wither.
     
  2. Go to the House of the Question and gain Salt's attention.
     
  3. Travel to the Salt Lions
     
  4. When Something Awaits you in Port, choose the bottom option that I can't remember the name of.
     
  5. Travel back to London with your Searing Enigma (and maybe additional Sphinxstone if you choose)
     
  6. Go to the University and sell it to the Alarming Scholar
     
  7. Cash money, money cash.

will put pictures here lsater

It is now about 2am and I'm tired I'll probably update this in the morning byee.